Determine the value of the following complex number power. Your answer will be plotted in orange. $ ({ e^{\pi i / 2}}) ^ {2} $
Answer: Since $(a ^ b) ^ c = a ^ {b \cdot c}$ $ ({ e^{\pi i / 2}}) ^ {2} = e ^ {2 \cdot (\pi i / 2)} $ The angle of the result is $2 \cdot \frac{1}{2}\pi$ , which is $\pi$ Our result is $ e^{\pi i}$.